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Translation Tessellation

Translation Tessellation
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2013-07-20 05:14
PolygonVectorTransformationGeometric Construction
In collections Translation Tessellation
This example demonstrates the creation of a tessellation pattern using translation transformations. It involves core mathematical concepts such as translation, congruence, vector operations, and polygon construction. The construction utilizes commands like Polygon, Segment, LineBisector, Point, Mirror, Vector, and Translate. It is suitable for high school mathematics education to understand the principles of transformation geometry and the formation of tessellations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 6) → poly1, a, F, b, c, d, e, f, C, D, E
  2. Segment(C, G) → g
  3. Segment(G, H) → h
  4. Segment(H, I) → i
  5. Segment(I, J) → j
  6. Segment(J, K) → k
  7. Segment(K, L) → l
  8. Segment(L, M) → m
  9. Segment(M, N) → n
  10. LineBisector(c) → p
  11. Segment(N, O) → q
  12. Segment(O, P) → r
  13. Segment(P, Q) → s
  14. Segment(Q, R) → t
  15. Point(p) → S
  16. Segment(R, S) → a_1
  17. Mirror(C, p) → C'
  18. Mirror(G, p) → G'
  19. Segment(C', G') → g'
  20. Mirror(G, p) → G'_1
  21. Mirror(H, p) → H'
  22. Segment(G'_1, H') → h'
  23. Mirror(H, p) → H'_1
  24. Mirror(I, p) → I'
  25. Segment(H'_1, I') → i'
  26. Mirror(I, p) → I'_1
  27. Mirror(J, p) → J'
  28. Segment(I'_1, J') → j'
  29. Mirror(J, p) → J'_1
  30. Mirror(K, p) → K'
  31. Segment(J'_1, K') → k'
  32. Mirror(K, p) → K'_1
  33. Mirror(L, p) → L'
  34. Segment(K'_1, L') → l'
  35. Mirror(L, p) → L'_1
  36. Mirror(M, p) → M'
  37. Segment(L'_1, M') → m'
  38. Mirror(M, p) → M'_1
  39. Mirror(N, p) → N'
  40. Segment(M'_1, N') → n'
  41. Mirror(N, p) → N'_1
  42. Mirror(O, p) → O'
  43. Segment(N'_1, O') → q'
  44. Mirror(O, p) → O'_1
  45. Mirror(P, p) → P'
  46. Segment(O'_1, P') → r'
  47. Mirror(P, p) → P'_1
  48. Mirror(Q, p) → Q'
  49. Segment(P'_1, Q') → s'
  50. Mirror(Q, p) → Q'_1
  51. Mirror(R, p) → R'
  52. Segment(Q'_1, R') → t'
  53. Mirror(R, p) → R'_1
  54. Mirror(S, p) → S'
  55. Segment(R'_1, S') → b_1
  56. Vector(C, A) → u
  57. Translate(C, u) → C'_1
  58. Translate(D, u) → D'
  59. Segment(C'_1, D') → c'
  60. Translate(C, u) → C'_2
  61. Translate(G, u) → G'_2
  62. Segment(C'_2, G'_2) → g'_1
  63. Translate(G, u) → G'_3
  64. Translate(H, u) → H'_2
  65. Segment(G'_3, H'_2) → h'_1
  66. Translate(H, u) → H'_3
  67. Translate(I, u) → I'_2
  68. Segment(H'_3, I'_2) → i'_1
  69. Translate(I, u) → I'_3
  70. Translate(J, u) → J'_2
  71. Segment(I'_3, J'_2) → j'_1
  72. Translate(J, u) → J'_3
  73. Translate(K, u) → K'_2
  74. Segment(J'_3, K'_2) → k'_1
  75. Translate(K, u) → K'_3
  76. Translate(L, u) → L'_2
  77. Segment(K'_3, L'_2) → l'_1
  78. Translate(L, u) → L'_3
  79. Translate(M, u) → M'_2
  80. Segment(L'_3, M'_2) → m'_1
  81. Translate(M, u) → M'_3
  82. Translate(N, u) → N'_2
  83. Segment(M'_3, N'_2) → n'_1
  84. Translate(N, u) → N'_3
  85. Translate(O, u) → O'_2
  86. Segment(N'_3, O'_2) → q'_1
  87. Translate(O, u) → O'_3
  88. Translate(P, u) → P'_2
  89. Segment(O'_3, P'_2) → r'_1
  90. Translate(P, u) → P'_3
  91. Translate(Q, u) → Q'_2
  92. Segment(P'_3, Q'_2) → s'_1
  93. Translate(Q, u) → Q'_3
  94. Translate(R, u) → R'_2
  95. Segment(Q'_3, R'_2) → t'_1
  96. Translate(R, u) → R'_3
  97. Translate(S, u) → S'_1
  98. Segment(R'_3, S'_1) → c_1
  99. Translate(C', u) → C''
  100. Translate(G', u) → G''
  101. Segment(C'', G'') → g''
  102. Translate(G'_1, u) → T
  103. Translate(H', u) → H''
  104. Segment(T, H'') → h''
  105. Translate(H'_1, u) → U
  106. Translate(I', u) → I''
  107. Segment(U, I'') → i''
  108. Translate(I'_1, u) → V
  109. Translate(J', u) → J''
  110. Segment(V, J'') → j''
  111. Translate(J'_1, u) → W
  112. Translate(K', u) → K''
  113. Segment(W, K'') → k''
  114. Translate(K'_1, u) → Z
  115. Translate(L', u) → L''
  116. Segment(Z, L'') → l''
  117. Translate(L'_1, u) → A_1
  118. Translate(M', u) → M''
  119. Segment(A_1, M'') → m''
  120. Translate(M'_1, u) → B_1
  121. Translate(N', u) → N''
  122. Segment(B_1, N'') → n''
  123. Translate(N'_1, u) → C_1
  124. Translate(O', u) → O''
  125. Segment(C_1, O'') → q''
  126. Translate(O'_1, u) → D_1
  127. Translate(P', u) → P''
  128. Segment(D_1, P'') → r''
  129. Translate(P'_1, u) → E_1
  130. Translate(Q', u) → Q''
  131. Segment(E_1, Q'') → s''
  132. Translate(Q'_1, u) → F_1
  133. Translate(R', u) → R''
  134. Segment(F_1, R'') → t''
  135. Translate(R'_1, u) → G_1
  136. Translate(S', u) → S''
  137. Segment(G_1, S'') → d_1

AI Drawing Prompt Reference

Draw a hexagon and then construct its side bisectors, use these bisectors as mirrors to reflect the hexagon repeatedly, creating a translation tessellation pattern that demonstrates translation, congruence, vector operations, and polygon construction.
The prompt above was compiled from the original drawing commands and is for reference only.